Orthogonal frequency division multiplexing access (OFDMA) ranging

ABSTRACT

A method for Orthogonal Frequency Division Multiplexing Access (OFDMA) ranging is provided. The method includes receiving a signal having OFDMA symbols. An FFT is performed on this signal. Matching ranging codes are found. The power for a given hypothesized ranging code is determined and compared to a power threshold to determine if the code was transmitted. The timing offset and power are reported as the result of ranging.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application claims priority to and incorporates by reference U.S.Provisional Application No. 60/717,049, filed Sep. 14, 2005, entitled“OFDMA Ranging”, Cory S. Modlin inventor.

STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT

Not applicable.

REFERENCE TO A MICROFICHE APPENDIX

Not applicable.

BACKGROUND

Embodiments of the invention are directed, in general, to communicationsystems and, more specifically, to ranging procedures for use incommunication systems.

Orthogonal Frequency Division Multiplexing Access (OFDMA) defines anaccess scheme of a two-dimensional grid that combines Time DivisionAccess (TDM) with Frequency Division Access (FDM). In OFDMA, datasymbols are delivered on subcarriers which form subchannels. Dependingon system situation, a predetermined number of subcarriers form onesubchannel.

Ranging is the term used to describe the procedure for an SS (subscriberstation) to join a network or to change BSs (base stations) as a resultof a hand-off. Ranging can also be used to update the frequency ortiming offset. However, it is expected that we will not use ranging forthis purpose and instead rely on updates from channel estimation.

For application of Time Division Duplexing (TDD) to the OFDMAcommunication system, ranging is required to acquire accurate timingsynchronization between the SS and the BS and adjust the reception powerof the BS on the uplink. In each OFDMA frame a ranging channel has aplurality of subchannels for transmitting a ranging signal.

The initial ranging is the process of acquiring a correct timing offsetbetween the BS and the SS and initially adjusting a transmit power. Uponpower-on, the SS acquires downlink synchronization from a receiveddownlink preamble signal. Then the SS performs the initial ranging withthe BS to adjust an uplink time offset and transmit power. The IEEE802.16d/e communication systems use the OFDM/OFDMA communication scheme.Thus, they perform a ranging procedure by transmitting a randomlyselected ranging code on a plurality of subchannels.

The periodic ranging is the process of periodically tracking the uplinktiming offset and received signal strength after the initial ranging.The SS randomly selects one of ranging codes allocated for the periodicranging in the ranging procedure.

SUMMARY

A method for Orthogonal Frequency Division Multiplexing Access (OFDMA)ranging is provided. The method includes receiving a signal having OFDMAsymbols. An FFT is performed on this signal. Matching ranging codes arefound. The power for a given hypothesized ranging code is determined andcompared to a power threshold to determine if the code was transmitted.The timing offset and power are reported as the result of ranging.

These and other features and advantages will be more clearly understoodfrom the following detailed description taken in conjunction with theaccompanying drawings and claims.

BRIEF DESCRIPTION OF THE DRAWINGS

For a more complete understanding of the disclosure and the advantagesthereof, reference is now made to the following brief description, takenin connection with the accompanying drawings and detailed description,wherein like reference numerals represent like parts.

FIG. 1 is a diagram illustrative of initial ranging slot, which may beeither 2 or 4 OFDMA symbols set by the BS in UL_MAP.

FIG. 2 is a diagram illustrative of periodic ranging showing three OFDMAsymbols with respective cyclic prefixes.

FIG. 3 shows mandatory PUSC tile configuration.

FIG. 4 is a graph showing the maximum correlation between ranging codesover 16 consecutive ranging codes.

FIG. 5 shows the round-trip delay as a function of distance to the BS.

FIG. 6 is illustrative of a two slot ranging allocation which share thesame subchannel(s) with the received signal.

FIG. 7 is illustrative of two symbol ranging.

FIG. 8 is illustrative of two possible locations of the rangingtransmission assuming that symbol 1 has the highest power level.

FIG. 9 is a presentation of FIG. 243a from IEEE publication 802.16-2004corr. “Corrigendum to IEEE Standard for Local and Metropolitan AreaNetworks—Part 16: Air Interface for Fixed Broadband Wireless AccessSystems,” Corr1/D3, May 2005.

FIG. 10 is a diagram illustrative of the round trip delay suffered bysignals in a communication system.

FIG. 11A shows samples of interest for flowchart of FIG. 11B.

FIG. 11B is a flowchart in accordance with an embodiment of theinvention.

DETAILED DESCRIPTION

It should be understood at the outset that although an exemplaryimplementation of one embodiment of the disclosure is illustrated below,the system may be implemented using any number of techniques, whethercurrently known or in existence. The disclosure should in no way belimited to the exemplary implementations, drawings, and techniquesillustrated below, including the exemplary design and implementationillustrated and described herein, but may be modified within the scopeof the appended claims along with their full scope of equivalents.

In summary, embodiments of the invention use the following principles:

-   -   we use the FFT results from the normal FFT time slots and we do        not calculate additional FFT results;    -   if we find that the performance is not sufficient and we have        cycles to spare;    -   performance can be improved by using sliding window FFT; and    -   we assume we will have multiple passes at initial ranging        because the estimates made at very low SNRs are not as reliable        as those made at higher SNRs.

Ranging is part of the overall initialization. Initialization steps aredescribed in section (6.3.9) of the Institute of Electrical andElectronics Engineers (IEEE) Standard 802.16-2004 “Part 16: AirInterface for Fixed Broadband Wireless Access Systems,” October 2004 andIEEE Standard 802.16e “Part 16: Air Interface for Fixed and MobileBroadband Wireless Access Systems Amendment for Physical and MediumAccess Control Layers for Combined Fixed and Mobile Operation inLicensed Bands,” D9, June 2005. Both standards incorporated herein byreference.

The initialization steps include:

-   -   MS scans for radio channel.    -   MS listens to frame structure, identifies cyclic prefix length,        does timing recovery and synchronizes to the BS clock (in both        TDD and FDD formats).        -   standard requires MS be within 2% of BS frequency.    -   MS obtains time/frequency when it can transmit a ranging request        from UCD/UL_MAP messages.    -   MS performs ranging (Section 6.3.9.5.1 for OFDMA) and (Section        6.3.10.3.1).        -   1. MS sends CDMA code at reduced power level.            -   a. MS randomly selects a ranging slot within its backoff                window (specified in UCD).            -   b. MS randomly selects the CDMA code within a set of                allowed codes (as specified in UCD).        -   2. if no response from the BS, keep increasing the power            level at next random contention slot.        -   3. BS sends RNG-RSP and a CDMA allocation IE in the UL_MAP            (UIUC=14) to indicate it successfully received CDMA code and            BS allocates slot for periodic ranging.            -   a. BS does not know which MS sent the CDMA code, so it                sends a broadcast message with the CDMA code and the                OFDMA slot and the MS uses this to identify itself.            -   b. if broadcast RNG-RSP message in CDMA allocation IE                has status continue, the MS continues to send CDMA codes                as it did initially with updates to timing/power as                specified in the RNG-RSP message but in a periodic                ranging region.        -   4. BS sends RNG-RSP with status success and allocates            bandwidth for specific MS.        -   5. MS sends RNG-REQ message(s) in its allocated            time/frequency slot after receiving a RNG-RSP with a success            status and a bandwidth allocation from the BS in UL_MAP.    -   negotiate basic capabilities (SBC-REQ/RSP) (Sections        11.8.1/11.8.3).        -   a. FDD/TDD.        -   b. max transmit power.        -   c. FFT size (128, 512, 1024, 2048).        -   d. HARQ (Chase or IR).        -   e. BTC, STC, LDPC.        -   f. AAS diversity zone.        -   g. optional permutations.    -   authorization and security key exchange.    -   registration using REG-REQ/RSP (Section 11.7).        -   a. IP version.        -   b. ARQ.        -   c. MAC CRC.        -   d. . . .

Step 1 of Ranging (Section 8.4.7)

“MS Sends CDMA Code”

The UL_MAP specifies one or more groups of 6 (or optionally 8) adjacentsubchannels on which the contention-based ranging is done.Contention-based means that more than one MS could transmit using thesame subchannels at the same time. The UL_MAP also specifies the numberof OFDMA symbols on which to transmit the ranging sequence.

During ranging, MSs randomly select a ranging slot in which to send arandom pseudo-random bit sequence (PRBS) BPSK code. MSs that haverandomly selected the same ranging slot will be incontention—transmitting at the same time and in the same subcarriers.Because they select ranging codes at random, more than likely, the PRBSwill be different for different MSs.

Through ranging, the BS can determine:

-   -   the symbol timing offset caused by transmission delays;    -   the frequency offset between the BS and MS caused by Doppler        shift or by inaccuracies in the local oscillator;    -   whether or not a specific PRBS code is present;    -   the received power; and    -   the noise variance.

Using this information, the BS can send corrections back to the MS andthe MS can continue ranging until the power, timing, and frequency isaligned. If two MSs happen to send the same code at the same time in thesame subchannels, the algorithm presented here will probably detect thecode and report a corrupted timing offset. If this happens, both MSswill think the BS successfully heard them and both MSs will adjust theirpower and timing and transmit again. There is a danger that the MS powerwill then be too high or the timing offset too early so that thesubsequent MS transmission corrupts other MS transmissions. An MS thatdoes not receive a response to ranging transmission that comes inresponse to a BS ranging response should abort and start over.

Format of Initial Ranging Transmission: Time Domain

For initial ranging or handoff, either 2 or 4 OFDMA symbols areallocated for one ranging slot. The ranging Orthogonal FrequencyDivision Multiplexing Access OFDMA symbols are of the form shown in FIG.1, which is a diagram illustrative of initial ranging slot, which may beeither 2 or 4 OFDMA symbols set by the BS in UL_MAP. In FIG. 1, thereare two sets of symbols 110 and 120, “CP1” 111 and 114 is the cyclicprefix for the first OFDMA symbol 112 and 113 using PRBS code n and“OFDMA symbol1” is the Nfft point output of the IFFT for PRBS code n.The second set of symbols 120, are optional and represent the output forPRBS code n+1. Because of the way the symbols are put together, there isno phase discontinuity between the two symbols carrying the same PRBScode.

Format of Periodic Ranging Transmission: Time Domain

In addition to the initial ranging region, a periodic ranging region isalso defined. Unlike the initial ranging region, the cyclic prefix isappended as usual during periodic ranging. Therefore, to use theperiodic ranging region, the MS must already be aligned in time.Misalignment will cause distortion not only in the ranging subchannels,but also for other users. FIG. 2 shows three OFDMA symbols 215, 225, and235 with respective cyclic prefixes 211, 221, and 231.

The idea is that after timing and power adjustments, the MS would switchto the periodic ranging region for fine adjustments and to allow abetter estimate of the SNR by the BS.

Format of Ranging Transmission: Frequency Domain

A subchannel contains groups of tiles—each tile has 4 adjacentsubcarriers over 3 OFDMA symbols. For the optional Partially UsedSubchannelization (PUSC) permutation, a tile contains 3 adjacentsubcarriers over 3 OFDMA symbols. For the AAC permutation, a bin (likepart of a tile) contains 9 adjacent subcarriers over a variable numberof OFMDA symbols (1, 2, 3, or 6).

A Pseudo-Random Binary Sequence (PRBS) is defined as:x¹⁵+x⁷+x⁴+x¹+1with c_(k) defined as the output. The PRBS is initialized to the value:0,0,1,0,1,0,1,1,s0,s1,s2,s3,s4,s5,s6 where s6 is the LSB of the PRBSseed and s6:s0=UL_PermBase (sent in UCD).

A Code Division Multiple Access (CDMA) code is a series of 144 bits outof the PRBS. Code 0 is bits 0:143, code 1 is bits 144:287, code n isbits 144·n: 144·(n+1)−1. The MS should select a code randomly from theset of available codes as prescribed in the UCD message. Each subcarrieris modulated with X_(k)=+1 or −1 depending on the 0 or 1 output of thePRBS.

A ranging channel for the mandatory Partially Used Subchannelization(PUSC) contains at least one group of 6 subchannels, each subchannel has6 tiles of 4 subcarriers each for a total of 144 subcarriers(6*6*4=144). I assume that if more than one group of 6 subchannels isused, the PRBS sequence is repeated—not extended. For the optional PUSC,there are 8 tiles with 3 subcarriers each and 6 tiles persubchannel—again there are 144 subcarriers (8*3*6=144). For the AACpermutation, there are 9 subcarriers per bin, 8 subchannels per ranginggroup, and 1, 2, 3, or 6 bins per OFDMA symbol for 72, 144, 216, or 432bits.

The receiver detects the code by correlating the received sequence witheach of the possible ranging codes. Therefore, the more codes there are,the smaller the chance of a collision but the higher the processingrequirements.

Detection of the Code, Power, Delay, and Frequency Offset

A BPSK (+/−1) symbol modulates each of the subcarriers in the rangingslot. The BPSK sequence is selected from a PRBS seeded to match acertain ranging code as we mentioned earlier. Assuming the BPSK sequenceis denoted by X_(k) for OFDM tone k and the channel is denoted as H_(k),the channel output at time n can be written as

$\begin{matrix}{y_{n} = {{\frac{1}{N}\lbrack {\sum\limits_{k = {{- N}/2}}^{{N/2} - 1}{X_{k}H_{k}{\mathbb{e}}^{2{\pi j}\;{{n{({k + ɛ})}}/N}}}} \rbrack} + w_{n}}} & (1)\end{matrix}$where ε is the frequency offset expressed as a fraction of the tonespacing (Δf·N/F_(s)), W_(n) is assumed here as additive white complexGaussian noise, Nis the IFFT size (number of complex samples—up to 2048in OFDMA), Δf is the frequency offset in Hz, and F_(s) is the samplingfrequency in Hz. Here we assume the MS has locked to the BS clock. X_(k)is the value of the PRBS code and can take on the values +1 and −1.

When the cyclic prefix is sufficiently long to cover the channel delayor, as in the case of ranging, when the symbol is continuous with nophase discontinuity, the output of the DFT at the receiver (FFT) can bewritten as:

$\begin{matrix}{Y_{k} = {{X_{k}H_{k}\frac{\sin\;{\pi ɛ}}{N \times {\sin( {{\pi ɛ}/N} )}}{{\mathbb{e}}^{{{j\pi ɛ}{({N - 1})}}/N} \cdot {\mathbb{e}}^{{- {j2\pi}} \cdot l \cdot {k/N}}}} + I_{k} + W_{k}}} & (2)\end{matrix}$where I is the OFDM symbol timing offset in samples, I_(k) is theinterchannel interference caused by the frequency offset fromsubcarriers other than subcarrier k, and W_(k) is the noise term.

$\begin{matrix}{I_{k}{\sum\limits_{\underset{m \neq k}{m = {{- N}/2}}}^{{N/2} - 1}{X_{m}H_{m}\frac{\sin\;{\pi ɛ}}{N\;{\sin( {{\pi\lbrack {m - k + ɛ} \rbrack}/N} )}}{\mathbb{e}}^{{{j\pi ɛ}{({N - 1})}}/N}{\mathbb{e}}^{{- {{j\pi}{({m - k})}}}/N}{\mathbb{e}}^{{- {j2\pi}} \cdot l \cdot {k/N}}}}} & (3)\end{matrix}$

For example, at 125 km/hr and 3.5 GHz, the ICI is about 24 dB below thesignal level on each subcarrier (using a Doppler shift of 405 Hz and asubcarrier spacing of 11.2 kHz). For the same conditions, the ICI is 27dB below the signal for the wider 15.6 kHz tone spacing.

We can discern one user from another by using the CDMA code. For allpossible ranging codes (the BS decides on the number of possible codesto use for initial and periodic ranging), we multiply the receivedsignal, Y_(k), by the ranging code and find Z_(k)=Y_(k)×{circumflex over(X)}_(k) where {circumflex over (X)}_(k) is one of the ranging codes. Ifwe have selected a code that was transmitted, X_(k)×{circumflex over(X)}_(k) will always equal 1 because X_(k) is either +1 or −1 and weassume X_(k)={circumflex over (X)}_(k).

For a matching CDMA code, we can find the symbol offset, I, bycalculating

$\begin{matrix}{{Z_{k}Z_{k + 1}^{*}} = {{H_{k}H_{k + 1}^{*}\frac{\sin^{2}{\pi ɛ}}{\lbrack {N \times {\sin( {{\pi ɛ}/N} )}} \rbrack^{2}}{\mathbb{e}}^{{j2\pi} \cdot {l/N}}} + {{noise}\mspace{14mu}{terms}}}} & (4)\end{matrix}$The sin² term will be very close to 1 for Doppler shifts we areconsidering (−0.02 dB for the 405 Hz Dopper/11.2 kHz tone spacingexample).

The noise terms can be written, ignoring the sin² and phase terms,noiseterms≈W_(k)H_(k+1)*+H_(k)W_(k+1)*+W_(k)I_(k+1)*+I_(k)W_(k+1)*+H_(k)I_(k+1)*+I_(k)H_(k+1)*+I_(k)I_(k+1)*+W_(k)W_(k+1)*  (5)

We expect no correlation between the channel, H, and the additive noise,W, Also, the ICI terms, I, are well below the signal term. However,there could be correlation between W_(k) and W_(k+)1 depending on thenoise environment. But it is unlikely that this correlation wouldpersist over many tiles.

If we assume the channel changes very little from subcarrier k to k+1and we assume that the noise is well below the signal, the symbol timingoffset is the phase of Z_(k)·Z*_(k+1)1 as seen in equation (4).

Turning now to FIG. 3 which is a diagram showing mandatory PUSC tileconfiguration. If a tile contains subcarriers t0 through t0+3, as shownin FIG. 3, we form the sumZ_(t0)Z_(t0+1)*+Z_(t0+1)Z_(t0+2)*+Z_(t0+2)Z_(t0+3)*for each tile and repeat the sum for all tiles. This can be written as

$\begin{matrix}{{{ZZ}^{*}\mspace{11mu}{sum}} = {\frac{1}{M}{\sum\limits_{i = 0}^{L - 1}\;\lbrack {\sum\limits_{n = 0}^{N - 2}\;{Z_{{ti} + n}Z_{{ti} + n - 1}^{*}}} \rbrack}}} & (6)\end{matrix}$where i is tile number index, L is number of tiles, ti denotes the firstsubcarrier of tile i, n is subcarrier index, N is number of subcarriersper tile and M=L*N−1). Each term in the sum is the multiplication of the“Z” term on a given subcarrier with the complex conjugate of the “Z”term on the adjacent subcarrier where “*” means complex conjugate.

From equation (4), we see that the phase of the ZZ* sum yields anestimate of the timing offset. Similarly, the magnitude of ZZ* sum givesan estimate of the transmit power and can be used to detect whether ornot the code is present.

If other users are in contention but are using different codes or wehave hypothesized the wrong code, the signal part of the sum ofZ_(k)·Z*_(k+1) will average to near zero if the codes are trulyorthogonal. In practice, however, the codes are not orthogonal as wediscuss later in this document. The ICI and noise terms will fall belowthe signal term as we average over more terms.

To get a feel for the performance of the signal and noise estimatesusing the sum in equation (6), we consider the case where there is onlyadditive Gaussian noise. In this case,

$\begin{matrix}{{{ZZ}^{*}{sum\_ just}{\_ noise}} = {\frac{1}{M}{\sum\limits_{i = {\#\mspace{11mu}{tiles}}}\lbrack {\sum\limits_{n = {0:\;{{nsubcarriersPerTile} - 1}}}{W_{{ti} + n}W_{{ti} + n + 1}^{*}}} \rbrack}}} & (7)\end{matrix}$because all other terms in equations (4) and (5) are zero when there isonly noise. If we assume there are enough terms in the sum in equation(7) so that the central limit theorem applies, the distribution of theabsolute value of ZZ*sum_just_noise is approximately Rayleigh. If we letthe power of the additive complex Gaussian noise be σ², then theexpected value of the absolute value of ZZ*sum_just_noise isapproximately:

$\overset{\_}{{{ZZ}^{*}{sum\_ just}{\_ noise}}} = {\frac{\sigma^{2}}{\sqrt{2}}\sqrt{\frac{\pi}{2}}\frac{1}{\sqrt{M}}}$which means that the noise level of the sum is reduced from the actualnoise level by

$\frac{\sqrt{\pi}}{2\sqrt{M}}.$

TABLE 1 Average power of the additive noise term in ZZ*sum relative tothe AWGN noise power. M = 108, 90, and 36 corresponds to 6, 5, and 2subchannels per ranging slot respectively with four subcarriers pertile. noise estimate from taking the absolute value of ZZ*sum_just_noiserelative to M actual noise power level 108 −10.7 dB 90 −10.3 dB 36  −8.3dB

Unfortunately, because the mean of the absolute value ofZZ*sum_just_noise is approximately Rayleigh, the values can vary widely.The cumulative distribution function of a Rayleigh random variablegenerated from a complex Gaussian random variable with variance σ² is:F _(R)(r)=1−e ^(−r) ² ^(/√{square root over (2)}σ) ² for r≧0.

From this, we can calculate the probability that the measured noiseexceeds the actual noise by a given amount. Irrespective of M and σ2,the probability that the measured noise exceeds the mean level, asmeasured in ZZ*sum_just_noise, by more than 4.9 dB is 1/1000 and by morethan 4.1 dB is 1/100. Simulation shows that this result holds for M aslow as 36.

The conclusion is that if we use |ZZ*sum| as the estimate of the signalpower, the average measured noise power will be below the actual noisepower by the values listed in Table 1 (about 8-10 dB). With a 1/1000chance, the measured noise will not exceed this by more than 4.9 dB. ForM=108, assuming we know the noise power, if we see a symbol with ameasured power higher than 10.7-4.9 dB below the noise power, there is a999/1000 chance that this symbol contained a ranging code and if we usethis as the threshold, there is a 1/1000 chance of a false detect. Wewill discuss how we measure the noise power later.

Multiple Antennas

Multiple receive antennas can be used to improve the performance ofranging. One simple way to take advantage of multiple antennas is toextend equation (6) over all receive antennas

$\begin{matrix}{{{ZZ}^{*}\mspace{11mu}{sum}} = {\frac{1}{M}{\sum\limits_{a = 0}^{A - 1}{\sum\limits_{i = 0}^{L - 1}\lbrack {\sum\limits_{n = 0}^{N - 2}{Z_{{ti} + n}^{a}Z_{{ti} + n + 1}^{*a}}} \rbrack}}}} & (8)\end{matrix}$where a denotes the antenna number, A is number of antennas, i is tilenumber index, L is number of tiles, ti denotes the first subcarrier oftile i, n is subcarrier index, N is number of subcarriers per tile₁₃andM is nowM=A*L*(N−1).If the noise from antennas is independent, the performance will improve.The noise reduction is proportional to the sqrt(M) as we describedearlier. Each term in the sum is the multiplication of the “Z” term on agiven subcarrier with the complex conjugate of the “Z” term on theadjacent subcarrier where “*” means complex conjugate.Code Correlation

Using contention-based ranging, we correlate the received signal witheach of the possible ranging codes. If there is correlation among codes,the power we detect for unused codes can be well above the noise level.

We ran a simple simulation assuming that there are 16 possible rangingcodes in a ranging domain. We looked over all 255 possible domains(selection of UL_PermBase). For any two codes, we summed up the dotproduct of the codes. Perfect correlation would yield a sum of 144.Perfect orthogonality would yield a sum of 0. The actual correlation isequal to the sum divided by 144.

Referring now to FIG. 5, which is a graph showing the maximumcorrelation between ranging codes over 16 consecutive ranging codes. Aswe see in FIG. 5, the codes do not have very good cross-correlationproperties. Depending on the selection of UL_PermBase, with 16 adjacentcodes, the correlation is between −5 and −7.5 dB.

This result assumes a flat channel. With a shaped channel, thecorrelation will change depending on how the correlation between codescorresponds with the highs and lows of the channel magnitude.

The correlation limits the number of users who can be detectedsimultaneously. Signals from different users will be received atdifferent powers.

Code Detection

In this section, we discuss the process of detecting whether or not aspecific ranging code is present.

The first step is to establish a reference. We propose allocating aregion that is one OFDMA symbol long and one ranging group in frequencyin which no MS is allowed to transmit. In this region, we can measurethe power level over the ranging subchannels and the result should bethe noise level. This region need not be allocated every frame and sothe bandwidth reduction will be extremely small.

If there are M complex subcarriers used to measure the overall noisepower, we can calculate the variance of the noise estimate. It is equalto

${{variance}\mspace{14mu}{of}\mspace{14mu}{noise}\mspace{14mu}{estimate}} = {\sigma^{2}{\sqrt{\frac{1}{M}}.}}$Then assuming the estimate itself is Gaussian, we can use the Gaussianerror function to calculate the probability that the noise estimateexceeds the actual noise level. We found that the probability that theestimated noise level exceeds the true noise power by 1 dB for 144subcarriers is about 1/1000. We therefore use +/−1 dB as our confidenceinterval. If we average over multiple regions, the estimate will becomemore accurate.

For each of the possible ranging codes in the initial ranging domain, weestimate the power in every OFDMA symbol using the absolute value ofZZ*sum as we described earlier. For each ranging code, n, we find thesymbol with the highest power, maxpwr(n). We say that a ranging code maybe present if maxpwr(n)>estimated noise level+1 dB+4.9 dB where 4.9 dBis the level at which there is a 1/1000 chance that the absolute valueof ZZ*sum will exceed when no ranging code is present—the 4.9 dB wasderived above.

Simply measuring a signal level greater than then noise does indicatethat some ranging code is present, but it does not necessarily mean thatthe specific ranging code, n, is present. The reason is the inter-codecorrelation as we discussed earlier. As we showed in FIG. 4, theinter-code correlation varies depending on UL_PermBase but is in the−7.5 dB to −5 dB range for a flat channel and could be different (worseor better) depending on the shape of the channel.

If we knew the cross correlation between all P ranging codes, r(ni, nj),we could calculate the received power of each code independently.

$\lbrack \begin{matrix}{\max\;{{pwr}(0)}} \\{\max\;{{pwr}(1)}} \\\vdots \\{\max\;{{pwr}( {P - 1} )}}\end{matrix} \rbrack = \mspace{574mu}\mspace{20mu}{\lbrack \begin{matrix}1 & {r( {{n\; 0},{n\; 1}} )} & \ldots & {r( {{n\; 0},{n( {P - 1} )}} )} \\\; & 1 & \; & \; \\\vdots & \; & ⋰ & {r( {{n( {P - 2} )},{n( {P - 1} )}} )} \\{r( {{n( {P - 1} )},{n\; 0}} )} & \ldots & {r( {{n( {P - 1} )},{n( {P - 2} )}} )} & 1\end{matrix} \rbrack\lbrack \begin{matrix}{{actpwr}(0)} \\{{actpwr}(1)} \\\vdots \\{{actpwr}( {P - 1} )}\end{matrix} \rbrack}$ max  pwr = R ⋅ actpwrThe cross correlation matrix, R, is symmetric. The actual power can thenbe calculated as:actpwr=R⁻¹ maxpwr.  (9)Unfortunately, however, we don't know the cross correlation matrix. Butwe can calculate the worst case correlation assuming a flat channel andassume r(ni, nj)=worst case correlation for all values. The matrixinverse can then be calculated off-line and we can approximate theactual power this way.

We calculate the actual powers in this way and determine that a specificcode is present if the actual power is within 4.5 dB of the highestactual power (the number 4.5 will likely need tweaking).

To calculate the frequency offset, we use the results of successiveFFTs. Only one MS can transmit at a time to estimate the frequencyoffset. The time domain signal due to a single input subcarrier, i, is(similar to equation (1) but for only one subcarrier, i)

$\begin{matrix}{y_{i,n} = {{\frac{1}{N}\lbrack {X_{i}H_{i}{\mathbb{e}}^{{j2\pi} \cdot {{n{({{\mathbb{i}} + ɛ})}}/N}}} \rbrack} + w_{n}}} & (10)\end{matrix}$and the corresponding frequency domain FFT output, on tone k due to aninput on subcarrier i with a time delay, I, is, using the definition ofthe DFT,

$\begin{matrix}{Y_{i,k} = {{\frac{1}{N}{\sum\limits_{n}{X_{i}H_{i}{\mathbb{e}}^{{j2\pi} \cdot {({n - l})} \cdot {{({{\mathbb{i}} + ɛ})}/N}}{\mathbb{e}}^{{- {j2\pi}} \cdot {{nk}/N}}}}} + W_{k}}} & (11)\end{matrix}$and the overall DFT, Y_(k), is the sum of Y_(i,k) over all i. As pointedout in “A Technique for Orthogonal Frequency Division MultiplexingFrequency Offset Correction” by Paul H. Moose; IEEE TRANSACTIONS ONCOMMUNICATIONS, VOL. 42. NO. 10; OCTOBER 1194, Y_(k,k) is dominant overthe Y_(k,i) terms for i≠k as intuition would suggest. With no frequencyoffset, the signal part of Y_(k,i)=0 for i≠k.If we take the DFT of y_(i,n+N+m), where N+m is the offset of one FFTrelative to the next, the result, U_(i,k), is

$\begin{matrix}\begin{matrix}{U_{i,k} = {{\frac{1}{N}{\sum\limits_{n}{X_{i}H_{i}{\mathbb{e}}^{{{j2\pi} \cdot {({n - l + N + m})}}{{({{\mathbb{i}} + ɛ})}/N}}{\mathbb{e}}^{{- {j2\pi}} \cdot {{nk}/N}}}}} + W_{k}}} \\{= {\frac{1}{N}{{\mathbb{e}}^{{{j2\pi} \cdot {({N + m})}}{ɛ/N}} \cdot {\mathbb{e}}^{{j2\pi} \cdot m \cdot {{\mathbb{i}}/N}}}Y_{i,k}}}\end{matrix} & (12)\end{matrix}$and then U_(k) is the sum of U_(k,i) over all subcarriers, i:

$\begin{matrix}{U_{k} = {\sum\limits_{i}{\frac{1}{N}{{\mathbb{e}}^{{{j2\pi} \cdot {({N + m})}}{ɛ/N}} \cdot {\mathbb{e}}^{{j2\pi} \cdot m \cdot {{\mathbb{i}}/N}}}Y_{i,k}}}} & (13)\end{matrix}$To estimate the frequency offset, we use a similar technique to the onewe used to detect the symbol offset. We define T_(k)=U_(k)×{circumflexover (X)}_(k) where {circumflex over (X)}_(k) is one of the hypothesizedranging codes, then

$\begin{matrix}\begin{matrix}{{Z_{k,k}T_{k,k}^{*}} = {{H_{k}{\mathbb{e}}^{{- {j2\pi}} \cdot l \cdot {k/N}}H_{k}^{*}{\mathbb{e}}^{{{- {j2\pi}} \cdot {({N + m})}}{ɛ/N}}{\mathbb{e}}^{{- {j2\pi}} \cdot m \cdot {k/N}}{\mathbb{e}}^{{j2\pi} \cdot l \cdot {k/N}}} + \ldots}} \\{= {{H_{k}H_{k}^{*}{\mathbb{e}}^{{{- {j2\pi}} \cdot {({N + m})}}{ɛ/N}}{\mathbb{e}}^{{- {j2\pi}} \cdot m \cdot {k/N}}} + \ldots}}\end{matrix} & (14)\end{matrix}$and then the angle of the sum is −(1+m/N)ε−mk/N from which we anestimate the frequency offset, ε.

This technique can only be used when there is no contention. Withcontention, there is no way to discriminate between users.

Timing Offset

Ranging Region and Cell Radius

Turning now to FIG. 9, which is FIG. 243a of IEEE publication802.16-2004 corr. “Corrigendum to IEEE Standard for Local andMetropolitan Area Networks—Part 16: Air Interface for Fixed BroadbandWireless Access Systems,” Corr1/D3, May 2005; incorporated herein byreference teaches that a series of ranging slots can be concatenated toform a ranging allocation. The allocation 920 spans both frequency andtime. In frequency, each ranging slot occupies one or more subchannelsso multiple ranging slots can occupy the same OFDMA symbol by using moresubchannels. Similarly, in time, a ranging slot occupies 1, 2, 3, or 4OFDMA symbols (2 or 4 for initial ranging, 1 or 3 for periodic ranging)and multiple slots can be concatenated in time. In the figure, eachnumber (0-11) represents one ranging slot 910.

The total number of OFDMA symbols for the ranging allocation 920 isspecified in the UL_MAP_IE. This number can be greater than the numberof symbols used by the ranging slots. This empty time is shown in FIG. 9as 930. The empty time is required during initial ranging to prevent adelayed transmission from colliding with data transmissions from otherMSs.

The number of empty symbols is related to the round-trip delay and thecell radius. Initially, the MS listens to the frame structure and shouldtransmit so as to be co-located with the BS. Practically, this meansthat the MS transmission can be anywhere from perfectly aligned (if theMS and BS are actually right next to each other) to delayed by an amountequal to the round-trip delay at the edge of the cell. The round-tripdelay is calculated as:round trip delay(μs)=distance(km)/c×10⁹where c=3×10⁸ m/s (speed of light). FIG. 5 shows the round-trip delay asa function of distance to the BS.

The concatenation of ranging slots places limits on the maximumsupported cell radius. If, for example, two symbol initial ranging slotsare used and slots are concatenated in time, there is no way todifferentiate between a ranging transmission delayed by more than 2symbols and a ranging transmission in the next slot delayed by less than1 symbol. This is illustrated in FIG. 6.

One way to address this problem is for the MS to recognize its CDMA codein slots beyond which it transmitted—for example, if the MS sends code Xin slot Y and the BS detects code X in slot Y+1, then the MS should besmart enough to recognize that code X in slot Y+1 means code X in slot Ywith an additional 2 symbol delay. It would be possible to exceed a twosymbol delay if N1 in FIG. 9 were set to 2 and the total rangingallocation were 5 (or more) symbols. But this would prevent us fromconcatenating more than one ranging slot in time.

FIG. 6 is illustrative of a two slot ranging allocation which share thesame subchannel(s) with the received signal 630. If the round-trip delayis equal to two full symbols, there would be no way to know if it wasslot m with a two symbol delay or slot n with no delay.

The number of OFDMA symbols we need to allocate for ranging is2+ceiling(round trip delay/symbol duration). Otherwise, the rangingtransmission will collide with data from another MS in a future OFDMAsymbol. The collision could cause distortion in all subcarriers, notjust the ranging subcarriers.

Estimating the Timing Offset

Our proposal is to keep the FFT time slots in their normal locations intime. Using a sliding window FFT approach will not work becausedistortion from other users will impede code detection.

In each OFDMA symbol used for ranging, we get a power and timing offsetestimate using equation (6). From this, we need to figure out where thereceived ranging signal actually falls. In FIG. 7, we look at an exampleof 2-symbol initial ranging. There are four possible FFT time slots forthe 2-symbol signal due to the round-trip delay.

Table 2 lists the delay that will be reported (assuming no noise ordistortion) as well as the attenuation of the measured signal power for2-symbol initial ranging. In reporting the attenuation, we assume thatif an OFDMA symbol is received that only overlaps the FFT time slot forx % of the time, the power attenuation is 10*log 10(x/100). This is onlyan approximation—there will be additional attenuation because of thedistorted ranging code correlation. When the OFDMA symbol does not fullyoverlap the FFT slot, there will be distortion in the delay estimate.

The delay of the two symbols can be derived by examining the power anddelay results from all four FFT slots. FIG. 7 is illustrative of twosymbol ranging. Brackets 712, 714, 716, and 718 show reference FFTlocations at the receiver. 720, 730 and 740 show possible ways rangingslots can be received.

TABLE 2 For each of the four FFT time slots, this table shows the(ideal) reported delay and the average attenuation of the signalcomponent due to misalignment within that slot. This is for an FFT sizeof 2048 and cyclic prefix of 256 (⅛). In general, ranging needs to workfor all FFT size and CP combinations. slot 0 slot 1 slot 2 slot 3 actualattenuation attenuation attenuation attenuation RT delay reported delaydB reported delay dB reported delay dB reported delay dB 0 0 0.00 17920.00 1536 X 1280 X 256 256 0.00 0 0.00 1792 X 1536 X 512 512 −0.58 2560.00 0 −9.03 1792 X 768 768 −1.25 512 0.00 256 −6.02 0 X 1024 1024 −2.04768 0.00 512 −4.26 256 X 1280 1280 −3.01 1024 0.00 768 −3.01 512 X 15361536 −4.26 1280 0.00 1024 −2.04 768 X 1792 1792 −6.02 1536 0.00 1280−1.25 1024 X 2048 0 −9.03 1792 0.00 1536 −0.58 1280 X 2304 256 X 0 0.001792 0.00 1536 X 2560 512 X 256 −0.58 0 0.00 1792 −9.03 2816 768 X 512−1.25 256 0.00 0 −6.02 3072 1024 X 768 −2.04 512 0.00 256 −4.26 33281280 X 1024 −3.01 768 0.00 512 −3.01 3584 1536 X 1280 −4.26 1024 0.00768 −2.04 3840 1792 X 1536 −6.02 1280 0.00 1024 −1.25 4096 0 X 1792−9.03 1536 0.00 1280 −0.58 4352 256 X 0 X 1792 0.00 1536 0.00 4608 512 X256 X 0 0.00 1792 0.00

This example can be extended to L symbols.

Assume we have power estimates, pwr(i), and symbol timing offsetestimates, delay(i) for each ranging code in symbol i where i=0 . . .L−1. The problem to solve is to find the actual delay and power for thepresent ranging code.

Our proposal is to do the following. Find the OFDMA symbol with thelargest power, pwr(imax). Assume that delay(imax) is a reliable delayestimate. Because the same ranging code is sent over two consecutiveOFDMA symbols, the actual delay could be eitherimax*(N+cpLen)+delay(imax)orimax*(N+cpLen)+delay(imax)−N

FIG. 8 is illustrative of two possible locations of the rangingtransmission assuming that symbol 1 has the highest power level. Forexample, looking at FIG. 8, assume that the highest power is measured insymbol 1 and that delay(1)=cpLen. The two possible actual locations ofthe received ranging signal are shown. In the first case, the rangingsignal overlaps symbol 0 by cpLen samples, overlaps symbol 1 completely(with N samples), and overlaps symbol 2 with N−cpLen samples. We canwrite this asoverlap1=[cpLen, N, N−cpLen].Similarly for the second possible locationoverlap2=[N, N, 0].To find the most likely actual location, we take the weighted average ofthe estimated powers formingoverlap1.* [pwr(0) pwr(1) pwr(2)]andoverlap2.* [pwr(0) pwr(1) pwr(2)]whichever is larger, we assume is the actual location.

FIG. 10 is a diagram illustrative of the round trip delay suffered bysignals in a communication system. Ranging adjusts each SS's timingoffset such that it appears to be co-located with the BS. The SS may setits initial timing offset to the amount of internal fixed delayequivalent to co-locating the SS next to the BS. This amount includesdelays introduced through a particular implementation and includes thedownlink DL PHY interleaving latency, if any.

Initial timing offset of received ranging signal can vary by as much asthe round trip delay and may be a multiple OFDMA symbols depending onradius. BS searches over entire time in which the ranging signal couldbe received. Guard time must be included in frame format to preventcollisions of ranging signal with normal data. The complexity increasesas round trip delay (cell radius) increases.

FIG. 11A shows samples of interest for flowchart of FIG. 11 B. Showingthat all symbols X₀ to X₅ are collected from three samples.

FIG. 11B is a flowchart in accordance with an embodiment of theinvention. Method 1100 begins 1110 by performing a Fast FourierTransform (FFT) 1120 in normal time slots upon the samples of interest1101. Sliding window or additional FFT results are not necessary andadds to complexity and lower performance. Upon performing FFT andgetting a frequency-domain signal, the circular shift becomes phasedrift. Ranging codes are extracted at 1130. A ranging code hypothesis1145 is compared to the extracted codes. Phase drift is detected 1150 byaveraging ZZ* across all tiles. A delay calculation is made by takingarctan of ZZ*. The power estimates for each ranging code are collected1160. Decorrelation 1160 is done by multiplying the power for up to Pcodes by a matrix as described in above paragraphs. A determination ifCDMA code is present is made, considering all possible time slots bydetermining if the power for a given code is above a threshold 1180. IfCDMA code is present, the most likely actual timing offset is determinedand delay calculation made.

While several embodiments have been provided in the disclosure, itshould be understood that the disclosed systems and methods may beembodied in many other specific forms without departing from the spiritor scope of the disclosure. The examples are to be considered asillustrative and not restrictive, and the intention is not to be limitedto the details given herein, but may be modified within the scope of theappended claims along with their full scope of equivalents. For example,the various elements or components may be combined or integrated inanother system or certain features may be omitted, or not implemented.

Also, techniques, systems, subsystems and methods described andillustrated in the various embodiments as discrete or separate may becombined or integrated with other systems, modules, techniques, ormethods without departing from the scope of the disclosure. Other itemsshown or discussed as directly coupled or communicating with each othermay be coupled through some interface or device, such that the items mayno longer be considered directly coupled to each other but may still beindirectly coupled and in communication, whether electrically,mechanically, or otherwise with one another. Other examples of changes,substitutions, and alterations are ascertainable by one skilled in theart and could be made without departing from the spirit and scopedisclosed herein.

1. A method for Orthogonal Frequency Division Multiplexing Access(OFDMA) ranging in a communication system, said method comprising:receiving, at a base station (BS), a signal having a plurality of OFDMAsymbols; performing, at the BS, a Fast Fourier Transform (FFT) on saidplurality of OFDMA symbols; extracting, at the BS, a plurality ofranging codes from the results of said FFT; finding, at the BS, rangingcodes matching a ranging code hypothesis; calculating, at the BS,Z_(k)Z*_(k+1), where Z_(k)=Y_(k)×{circumflex over (X)}_(k), {circumflexover (X)}_(k) is one of the ranging codes and Y_(k) is the receivedsignal, where k denotes subcarrier number and Z_(k)Z*_(k+1), is theproduct Z_(k) and the complex conjugate of Z_(k+1) where “*” means thecomplex conjugate; summing, at the BS, Z_(k)Z*_(k+1) values over allsubcarriers k, for which subcarriers k and k+1 are both subcarriers usedfor ranging; estimating, at the BS, a transmit power by using themagnitude of said sum; and determining, at the BS, if the power for agiven code is above a threshold.
 2. The method of claim 1, wherein saidthreshold is set relative to noise measured in unused subchannels. 3.The method of claim 1, wherein multiple receive antennas and receivedsignals are used and the sum is${{ZZ}^{*}\mspace{11mu}{sum}} = {\frac{1}{M}{\sum\limits_{a = 0}^{A - 1}{\sum\limits_{i = 0}^{L - 1}\lbrack {\sum\limits_{n = 0}^{N - 2}{Z_{{ti} + n}^{a}Z_{{ti} + n + 1}^{*a}}} \rbrack}}}$where a denotes the antenna number, A is number of antennas, i is tilenumber index, L is number of tiles, t_(i) denotes a first subcarrier oftile i, n is subcarrier index, N is number of subcarriers per tile andZZ*, is the product Z and the complex conjugate of Z where “*” means thecomplex conjugate andM=A*L*(N−1).
 4. The method of claim 1 further comprising: calculating,at the BS, the delay of said received signal.